Physics 132 4/24/13 Prof. E. F. Redish 1 4/24/13 1 Physics 132 Theme Music: Arvo Pärt Spiegel im Spiegel (Mirror in Mirror) Cartoon: Virgil Partch April 24, 2013 Physics 132 Prof. E. F. Redish 4/24/13 2 Physics 132 9.1 9.2.1 9.2.2 9.3 A 0% 85% 10% 10% B 10% 10% 60% 85% C 90% 0% 20% 10% D 0% 5% 5% 0% E 0% 0% 5% 0%
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Theme Music: Arvo Pärt Spiegel im Spiegel (Mirror in Mirror)€¦ · Physics 132 4/24/13 Prof. E. F. Redish 1 4/24/13 Physics 132 1 Theme Music: Arvo Pärt Spiegel im Spiegel (Mirror
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Physics 132 4/24/13
Prof. E. F. Redish 1
4/24/13 1 Physics 132
Theme Music: Arvo Pärt Spiegel im Spiegel (Mirror in Mirror)
Cartoon: Virgil Partch
April 24, 2013 Physics 132 Prof. E. F. Redish
4/24/13 2 Physics 132
9.1 9.2.1 9.2.2 9.3
A 0% 85% 10% 10%
B 10% 10% 60% 85%
C 90% 0% 20% 10%
D 0% 5% 5% 0%
E 0% 0% 5% 0%
Physics 132 4/24/13
Prof. E. F. Redish 2
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Foothold Ideas 1: The Physics
Certain objects (the sun, bulbs,…) give off light.
Through empty space (or ~air) light travels in straight lines.
Each point on an object scatters light, spraying it off in all directions.
A polished surface reflects rays back again according to the rule: The angle of incidence equals the angle of reflection.
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Foothold Ideas 2: The Psycho-physiology
We only see something when light coming from it enters our eyes.
Our eyes identify a point as being on an object when rays traced back converge at that point.
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Where does an object seen in a mirror appear to be?
object
Virtual image of the object
equal distance along perpendicular
What happens when a ray hits a curved mirror?
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A Spherical Mirror: Central Rays
center of sphere
All rays satisfy the “angle of incidence = angle of reflection” measured to the normal to the surface
All rays through the center strike the mirror perpendicular to the surface and bounce back along their incoming path.
A few rays are easy to figure out where they go.
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A Spherical Mirror: Central Ray
center of sphere
All rays satisfy the “angle of incidence = angle of reflection” measured to the normal to the surface
The ray hitting the central line of the diagram is particularly simple.
A few rays are easy to figure out where they go.
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A Spherical Mirror: Parallel Rays
center of sphere
A few rays are easy to figure out where they go.
All rays parallel to and near an axis of the sphere reflect through a single point on the axis (the focal point)
All rays satisfy the “angle of incidence = angle of reflection” measured to the normal to the surface
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Images in a Spherical Mirror: 1 Physical
center of sphere
focal point
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Kinds of Images: Real In the case of the previous slide, the rays
seen by the eye do in fact converge at a point. When the rays seen by the eye do meet,
the image is called real. If a screen is put at the real image, the rays
will scatter in all directions and an image can be seen on the screen, just as if it were a real object.
Reading questions What is the difference between the image points
and the focal point? Is the distance of the real image interpreted by our brain, or does it have a measurable distance from the mirror like the image and focal point?
Other then the three light rays mentioned in the reading, do the other light rays also line up on the image point? So if we know the ray parallel to the center line, the ray that bounces off the center point of the mirror and the ray with no incidence, can we see how every light ray will bounce off a mirror if they all go through the image point?
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o i
h
h´
RoiR
hh
oi
hh
!!=
=
'
'
R
2/111Rf
oif=+=
Mathematical
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Images in a Spherical Mirror: 2 Physical
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Kinds of Images: Virtual
In the case of the previous slide, the rays seen by the eye do not converge at a point.
When the rays seen by the eye extrapolate to a point but don’t actually meet, the image is called virtual.
In our case, the convergence point is behind the mirror.
If we look at the virtual image from behind the mirror, what will we see?
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o i
h h´
o i
R
oRiR
hh
oi
hh
+!=
=
'
'
2/111Rf
oif=!=
Mathematical
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Unifying Equation for Mirrors If we treat our mirror quantities as “signed” and let the
signs carry directional information, we can unify all the situations in a single set of equations.
2/'111Rf
oi
hh
oif==+=
h > 0 h´< 0 h < 0 h´> 0
i > 0 o > 0
i < 0 o < 0 f < 0
f > 0
“standard” arrangement
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Images in a Spherical Mirror: 2 Physical
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Simulations
Overview (lots of rays) – http://webphysics.davidson.edu/